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Table 2 Results of the proposed greedy algorithm (SEQ) versus the MIS-based algorithm and upper (UB) and lower bound (LB) as determined by Gurobi 5.6 solver within 3,000 s

From: Efficiently identifying critical nodes in large complex networks

Graph

k

LB

UB

SEQ

MIS

Graph

k

LB

UB

SEQ

MIS

ER125

5

405

405

851

715

ER150

5

4,277

4,277

4,972

5,471

ER125

10

133

133

151

199

ER150

10

837

2,301

2,678

4,862

ER125

15

66

66

76

81

ER150

15

347

347

976

890

ER125

20

36

36

44

43

ER150

20

167

167

220

410

ER125

25

20

20

23

24

ER150

25

94

94

101

201

ER125

30

9

9

12

15

ER150

30

58

58

69

124

ER125

35

3

3

7

10

ER150

35

36

36

44

79

ER125

40

0

0

2

5

ER150

40

22

22

29

52

ER125

45

0

0

0

0

ER150

45

14

14

16

36

ER125

50

0

0

0

0

ER150

50

8

8

11

22

BA200

5

818

818

818

1,073

BA250

5

782

782

782

1,235

BA200

10

297

297

298

668

BA250

10

342

342

342

626

BA200

15

156

156

156

413

BA250

15

221

221

221

462

BA200

20

104

104

104

304

BA250

20

143

143

143

355

BA200

25

70

70

70

206

BA250

25

105

105

105

293

BA200

30

48

48

48

164

BA250

30

77

77

77

243

BA200

35

33

33

33

135

BA250

35

60

60

60

213

BA200

40

20

20

22

114

BA250

40

45

45

45

183

BA200

45

15

15

17

98

BA250

45

30

30

30

158

BA200

50

10

10

12

77

BA250

50

21

21

23

135

WS100

5

2,766

4,465

4,465

4,465

WS125

5

4,578

7,140

7,140

7,140

WS100

10

1,054

2,941

4,005

4,005

WS125

10

1,796

6,005

6,555

6,555

WS100

15

572

945

3,570

1,784

WS125

15

892

3,642

5,995

5,995

WS100

20

379

495

3,160

1,107

WS125

20

618

3,187

5,460

5,460

WS100

25

234

300

2,775

578

WS125

25

433

708

4,950

1,719

WS100

30

176

219

2,415

414

WS125

30

309

467

4,465

758

WS100

35

132

148

2,080

271

WS125

35

239

344

4,005

480

WS100

40

98

103

1,770

159

WS125

40

195

246

3,570

370

WS100

45

70

72

1,485

94

WS125

45

152

180

3,160

278

WS100

50

48

48

1,225

67

WS125

50

117

137

2,775

207

FF125

5

3,237

3,643

3,874

5,280

FF150

5

5,895

7,789

7,660

7,789

FF125

10

872

1,805

2,202

2,588

FF150

10

2,362

9,591

6,252

6,711

FF125

15

318

318

1,198

515

FF150

15

1,491

7,893

5,087

5,819

FF125

20

165

165

773

249

FF150

20

911

3,909

4,043

5,192

FF125

25

111

111

422

158

FF150

25

561

1,967

3,359

4,319

FF125

30

73

73

118

103

FF150

30

339

1,237

2,322

3,869

FF125

35

46

46

65

69

FF150

35

216

380

1,874

693

FF125

40

29

29

40

45

FF150

40

159

174

1,275

344

FF125

45

16

16

25

31

FF150

45

105

117

793

240

FF125

50

11

11

15

21

FF150

50

79

79

321

155

  1. The networks are those presented in [20].